Geodesic
On a class of QI-rings
Glasgow mathematical journal, Tome 34 (1992) no. 1, pp. 75-81

Voir la notice de l'article provenant de la source Cambridge University Press

The concept of weak relative-injectivity of modules was introduced originally in [10], where it is shown that a semiperfect ring R is such that every cyclic right module is embeddable essentially in a projective right R-module if and only if R is right artinian and every indecomposable projective right R-module is uniform and weakly R-injective. We show that in the above characterization the requirement that indecomposable projective right R-modules be uniform is superfluous (Theorem 1.11). In this paper we further the study of weak relative-injectivity by considering the class of rings for which every right module is weakly injective relative to every finitely generated right module. We refer to such rings as right weakly-semisimple rings. The class of right weakly-semisimple rings includes properly all semisimple rings and is a subclass of the class of right QI-rings. A ring R is said to be a right QI-ring if every quasi-injective right R-module is injective. QI-rings have been studied in [2], [3], [4], [6], [7], [8], [11], among others. 
Jain, S. K.; López-Permouth, S. R.; Singh, Surjeet. On a class of QI-rings. Glasgow mathematical journal, Tome 34 (1992) no. 1, pp. 75-81. doi: 10.1017/S0017089500008557
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